On the Complementarity of the Harmonic Oscillator Model and the Classical Wigner–Kirkwood Corrected Partition Functions of Diatomic Molecules

Abstract

The vibrational and rovibrational partition functions of diatomic molecules are considered in the regime of intermediate temperatures. The low temperatures are those at which the harmonic oscillator approximation is appropriate, and the high temperatures are those at which classical partition function (with Wigner–Kirkwood correction) is applicable. The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

“…Note that for some molecules the two-term Wigner–Kirkwood correction is sufficient to treat similar temperatures. , Similar studies with a classical approach to partition functions are known for ArO and H 2 diatomics.…”

“…First, the RRHO values are systematically and significantly lower than Q int , g WK 3 , which means that anharmonicity of that radical is high and those two methods are not complementary as for example in case of the carbon monoxide molecule . Second, the values with negative contribution excluded are almost the same which means that the scattering states on the electronic ground PEC have negligible effect , as was discussed, this makes that method applicable for thermochemistry in the temperature range under consideration because scattering states virtually have no influence on calculated quantities.…”

“…The partition function will be calculated with the expression which takes into account all the interactions between atoms (bound, metastable, and scattering): ,,, where β = 1/( k B T ) is the inverse temperature, V is the potential energy function of the molecule, g ( ele ) is the multiplicity of a given electronic state, V ( ∞ ) the energy of dissociated atoms (see Figure ), and wk 3­( r ) the correcting Wigner–Kirkwood factor: , …”

“…At high temperatures, the classical method with Wigner–Kirkwood quantum corrections proves to be very convenient. − High temperature is understood as a temperature up to 6000 Kthis is a standard maximum temperature of NIST-JANAF Thermochemical Tables , and NASA polynomials (fitted to Gurvich data for which open access is not provided). The internal partition functions, on which thermodynamics is based, are also calculated up to 5000–8000 K in the ExoMol database. , …”